Gamification: Ability-Based Challenge

In a study of what makes video games so captivating, the key element was found to be variable ability-based challenge for players. Th e most popular games took players through increasingly challenging levels as they became more and more skillful. As skill improved, the next challenge motivated new mastery to just the right extent such that the player could reach the next goal with practice and persistence. Th e most motivating video games are ones in which players make the correct move about ...

 Maintain Positive Memories and Knowledge

Other ways to celebrate and maintain positive memories and knowledge include the following: Have students teach the new skill to someone else. Have students keep a list of achievements in their math journals or write them on a wall chart. Take a photo of the fi nal achievement (even if it is something as simple as a well-solved math problem). Have students compose a note to their parents, and add your own comments. Provide opportunities for students to transfer the new skills to new situatio...

 Learning Strengths: Map Readers and Explorers

I recognize Map Readers because they often like to work independently, but they are most comfortable when they have specifi c instructions or procedures to follow. Th ey often take more time and work deliberately, showing all their steps on homework or taking detailed notes in class or during group work. Explorers are the students who want to skip the detailed instructions and jump right into fi guring things out by trial and error. Th ese students are not likely to use estimation, even when ...

 How Brains Respond to Positive/Negative Feedback in Child...

In children up to eight or nine years old, the dopamine-modulating reward center in the nucleus accumbens reacts strongly to positive feedback (activating the prefrontal cortex) and minimally to negative feedback. In older children, increased activation still occurs in the PFC when dopamine is released in response to positive feedback (particularly in response to correct answers/ predictions). However, the greatest age-related change is the higher reactivity of the NAc to negative feedback an...

 Delay Method of Errorless Math Practice

Prepare a list of the calculations from the flash cards on a sheet of paper. These can be on a template, with multiplication facts at the appropriate level pulled and copied for the student. On these forms, include three columns next to each multiplication question, labeled “correct repeat,” “correct wait,” and “correct response.” Start with review and confi dence building. For example, show the question 3 × 4 = __ on the card and without any delay say the answer. Th e student repeats the que...

 Mathematical Cue Words

Addition: add, plus, sum, total, altogether, increased by, grew, gained, total of, combined, more than (as in, “3 more than 7 is 10”), put together, in all Subtraction: minus, take away, diff erence, less than, from, remove, subtract, gives away, sells, loses, fewer than, decreased by, diff erence between Multiplication: product, times, doubled (tripled, etc.), some problems give information about one and ask for total amounts (also, when dealing with multiplication of fractions, of usuall...

 Use a Big Opening for Class

In your planning, consider what you most want students to know and then work backward to develop an opening that promotes sustained interest toward that goal. If possible, represent the unit in several different ways that appeal to different learning strengths and levels of achievable challenge so you can continually engage all students. Here are some fascinating facts you can use as “big openings” with your students to help them with number sense, specifi cally with understanding large numb...

 Keeping Students Motivated Using Future Rewards

Periodically remind students that their mental effort is relevant to pleasure in the near future. The younger the children, the less tolerant their brains are to activities that are not pleasurable now or expected to be so in the very near future. Fortunately, the dopamine-reward network releases motivating dopamine in expectation of pleasure. Let students know which of their enjoyable math activities will be coming up during the lesson and how what they are practicing now connects to the des...

 Math Exercise: Comparisons

Select two boxes or cans of food that weigh 8 ounces and 16 ounces, respectively. Have students hold each as you tell them (or they read) the weights of the containers. Give students a box or can with the weight covered and have them compare the weight of the new package to the weight of the 8- and 16-ounce samples. Th ey can then estimate whether the new item’s weight is closer to 8 or 16 ounces. As students become more successful, they may want to predict a more specifi c weight. Ask them t...

 Math Games

Buzz. An example of a low-stress, win-win game is Prime Number Buzz. Students stand in a circle or at their desks and go around the room in order, saying either the next sequential number if it is a composite or “buzz” if it is a prime. If they are incorrect, they sit down, but they keep listening and when they catch another student’s error, they stand up and rejoin the game. (The same game format works for Multiples Buzz, using multiples of, for example, 3, 4, and so on.) Telephone. This is...

 Teaching Temperature

Outside Temperatures. Place a thermometer outside a window so students can make daily calculations and keep a chart reporting the actual temperature and the temperature change from the previous day. Students will see that the change can be a negative number without the temperature falling below 0—an often-confusing concept that is clarified by these observations. An achievable-challenge extension could include barometers, and students who need more advanced work can learn how negative—or fal...

 "This Is Not a..." Game

A game called “Th is Is Not a...” encourages multiple solutions and is played in a relaxed environment that encourages creativity. Students pass around an object—such as a toy telephone—and say, “This is not a....” Younger students name an object that is not a toy telephone (for example, “This is not a pencil.”). Older students continue and say, “This is not a toy telephone, it is a...,” and they gesture or mime to suggest the object that they are pretending the toy telephone is—perhaps a com...

 Math Exercise: Multiple Approaches to Problem-Solving

For example, if the problem was to fi nd the answer to 8 × 6, students may suggest three options: memorizing the multiplication table for 6, knowing that 8 × 5 = 40 and adding another 8 to equal 48, or adding a column of six 8s. Allowing students to personally choose among approaches all confi rmed as correct and to support their choice will increase their comfort levels. Th is process also builds math logic, intuition, and reasoning skills that extend into other academic subjects and real-li...